This paper presents exact solutions for the buckling loads and postbuckling states of extensible, shear deformable beams. The governing equation for the large-amplitude lateral deformation of beams in compression is expanded in Taylor series up to the cubic nonlinearity. Closed-form solutions in terms of the axial and shear stiffnesses are developed for statically determinate and statically indeterminate beams. Namely, pinned-pinned, cantilevered, clamped-clamped, and clamped-pinned beams are considered with the loaded end is a roller that is able to slide. The postbuckling response under a given axial load is exactly derived. The dependence of the buckling load on the length-to-radius of gyration is discussed. It is shown that the extensibility and the shear deformation significantly affect the buckling loads and the postbuckling response. For conventional materials with positive Poisson’s ratio, the inclusion of the axial and shear deformation results in a meaningful reduction of the buckling load. It is further shown that the buckling load can be enhanced by designing artificial metamaterials materials with an effective negative Poisson’s ratio.

本文提出了可伸展，剪切可变形梁的屈曲载荷和屈曲后状态的精确解。在压缩中，梁的大振幅横向变形的控制方程以泰勒级数展开，直至立方非线性。针对静定梁和静定梁开发了关于轴向刚度和抗剪刚度的封闭式解决方案。即，考虑将销钉销钉，悬臂梁，夹紧钳位钉和夹紧销钉梁的负载端作为能够滑动的滚子。精确推导了给定轴向载荷下的后屈曲响应。讨论了屈曲载荷对回转半径与半径的关系。结果表明，伸长率和剪切变形显着影响屈曲载荷和后屈曲响应。对于具有正泊松比的常规材料，轴向变形和剪切变形的加入可显着降低屈曲载荷。进一步表明，可以通过设计具有有效负泊松比的人造超材料来增强屈曲载荷。